Generation of over 1000 Diffraction Spots from 2D Graded Photonic Super-Crystals

For the first time, we are able to generate over 1000 diffraction spots from a graded photonic super-crystal with a unit super-cell size of 12a x 12a where a is the lattice constant and hole radii are gradually changed in dual directions. The diffraction pattern from the graded photonic super-crystal reveals unique diffraction properties. The first order diffractions of (+/- 1, 0) or (0, +/- 1) disappear. Fractional diffraction orders are observed in the diffraction pattern inside a square with vertices of (1, 1), (1, -1), (-1, -1) and (-1, -1). The fractional diffraction can be understood from lattices with a period of a. However, a dual-lattice model is considered in order to explain higher-order diffractions. E-field intensity simulations show a coupling and re-distribution among fractional orders of Bloch waves. There are a total of 12 x 12 spots in E-field intensity in the unit supercell corresponding to 12 x 12 fractional diffraction orders in the diffraction pattern and 12 x 12 fractional orders of momentum in the first Brillouin zone in k-space.